​​Is Cross-Index Generalization Achievable via Neural Calibration of Parametric Option Pricing Models?​

Abstract

​​Calibration of option pricing models has been widely studied, with research focusing both on developing accurate objective function optimizers and on methods for solving option pricing models efficiently. A large part of the calibration process consists not only of the parameters optimization but also of repeated option price calculations. To accelerate this process, I replace traditional pricing methods with a pre-trained neural network, aiming to reduce computation time while maintaining a high level of accuracy. The network is trained to approximate the pricing functions of the Bates (1991) and Heston (1993) models. I then investigate same index calibration performance and then study whether parameters calibrated on one equity index can be transferred to another (“cross-index generalization”) and still produce efficient predictions. I consider two U.S. equity indices, the S&P 500 and the Nasdaq 100 and follow a two-step process: the Forward Pass where the neural network is trained on synthetic data, which enables coverage of a wide range of parameters, enhancing generalization capacity of the neural network ; and the Backward Pass which combine the trained network with a Differential Evolution algorithm to calibrate model parameters on real market data. After calibrating each model on its respective index, results demonstrate good performance, especially for the first 10 to 15 weeks, with an expected growing predictive errors with time horizon. To extend the study, I analyze the distribution of prediction errors across different horizons ahead of the calibration week in order to detect model instabilities. The findings reveal that models are particularly unstable when predicting the Nasdaq option chain with parameters calibrated on itself for horizons between approximately the 15th and 25th weeks. Similarly, I detect instabilities when predicting the S&P 500 option chain with parameters calibrated on the same index between the 12th and 26th weeks. Following this study, I test cross-index predictions by using parameters calibrated on one index to predict the option chain of the other one. Results indicate no significant difference between cross-index and same-index predictions errors when S&P 500–calibrated parameters are used to predict Nasdaq options over horizons 13 to 27 weeks after calibration. However, this potential transferability contradicts the evidence of instability observed for same-index predictions within the same period, casting doubt on the existence of true cross-index generalization. Conversely, when Nasdaq-calibrated parameters are used to predict S&P 500 options over horizons 45 to 50 weeks, no significant difference is observed. However, same-index performance with these time horizons did not show substantial instability, leaving the possibility of cross-index generalization plausible under specific conditions. Although, in some cases cross index test results did indicate significant difference be- tween same index and cross index predictions errors for specific time horizons, cross index predictions errors remain relatively small in the short term horizons (especially when calibrating on the S&P 500 to predict the Nasdaq), therefore making the cross index calibration valid and useful depending on the level of accuracy required.​